Lie symmetries applied to interval integration

Abstract

In this paper, we propose a new approach for improving significantly existing guaranteed integration methods for state equations with uncertain initial conditions. We first find a tube that encloses the solution of the differential equation assuming that the initial state is known. Then, using Lie symmetries, we inflate the tube in order to contain the uncertainty associated with the initial state. The method is shown to be efficient on examples coming from reachability analysis and robotics.